Download Ideal Gas Law / Heat Transfer

AOS 101 Discussion
Val Bennington
Ideal Gases
September, 2008
REVIEW
 COUNTOURING- YOU LOVE IT!
 Helps gain a better sense of location and strength of
certain past or present weather features
 Time to put someone on the spot…
For temperature contouring…
 Gradient: the spatial rate of change of a given field (i.e. how close
are the lines together)
 Lines closely packed = steep gradient
 For isotherms, closely packed lines (temperature gradients) =
front.
For Pressure Contouring
 For isobars, closely packed lines = strong winds.
 Also, winds blow nearly parallel to isobars
 Counterclockwise around lows = cyclonic
 Clockwise around highs = anticyclonic
Station Model Homework
 Generally very good
 Couple of points to make
 Visibility- what is when it is clear?
 Winds – label to / from
Changing gears
 Robert Boyle
 Was the first to analyze the
behaviors of gases scientifically in
the 17th century
 He discovered that PV = constant if
temperature is also held constant
P
V
 This is now known as Boyle’s Law
Jacque Charles
 A French chemist who several years after Boyle
came to another important conclusion
 At a constant pressure, the volume of any gas is
directly proportional to the temperature:
 V/T = constant
 Thus, if we increase the temperature of a gas,
yet keep the pressure the same, the volume will
also increase.
One more French guy- Joseph
Louis Gay-Lussac
- 1802
- At a constant volume, the pressure of any gas is
directly proportional to the temperature (in degrees
Kelvin!):
P/T = constant
(at constant volume)
- Thus, if we increase the temperature of a gas, yet
keep the pressure the same, the volume will also
increase.
Combining these laws
 The Ideal Gas Law
PV = nRT
Or
P = ρRT (because ρ = m/V)
This is what is used in meteorology because it makes for
easier comparison by combining two variables into one
T constant: As P increases, ρ increases
P constant: As T increases, ρ decreases
ρ constant: As T increases, P increases
Variable Definitions
 P, Pressure: Force of the molecules that make up the gas,
exerted on the surface the gas is making contact with (per unit
area): P = Force/Area. Units:1 mb = 1 hPa
1 hPa = 100 Pascals (Standard Unit)
 T, Temperature: Average kinetic
energy of the molecules that
2
make up the gas. KE = 1/2mv scale = (K)
 ρ, Density: Mass per unit volume (of the gas analyzed). ρ =
m/V. The more molecules in a specific volume, the greater the
density. (kg/m3)
 R, The “gas constant for dry air”: 287 J/kg K
Ideal Gas Tutorial
Let’s try a calculation
 If the temperature of an air parcel is 252.5 K, and its
density is 0.690 kg/m^3, what is the pressure of the air
parcel?
 From the gas law, p = ρ *R * T
 T = 252.5 K
 ρ = 0.690 kg/m^3
 R = 287 J/kg K
 So, p = 0.690 * 252.5 * 287 = 50000 Pa
 In millibars, p ~ 500 mb
Heat Transfer
What Is Heat??? (Q)
 Heat is not the same as temperature!!!
 Heat is the energy that is transferred between
two objects of different temperature
 If two objects both have the same temperature
– the one with more mass has more heat
 Measured in Joules (kg*m2/s2) or Calories
Material Differences
 You add the same amount of heat to two different
objects (same size, both at the same initial temp)
 One’s temperature increases faster than the other’s
 Why???
Specific Heat (C)
 All materials have a specific heat
 Specific heat tells us how much energy we must add in
order to increase one gram of the one degree
 Expressed in J / kg / K
Heat Capacity
 But what if the two objects were different sizes?
 Lake Michigan vs. cup of water
 Which one do you need to add more heat to in order to
raise the temperature?
 Heat capacity is a measure of how well an object stores
heat
 HC = heat added / change in temp
What is Energy?
 Energy is the ability to do work
 The sum of all energies IS CONSTANT – it is neither
created or destroyed but merely changes form (First
Law of Thermodynamics)
Examples
 Water has a specific heat of 4180 J / kg / K
 Air has a specific heat of 1000 J / kg K
 How much heat must we add to raise 10 kg of water 10
degrees?
 Q = C * m * ΔT
 m = 10 kg, C = 4180 J/kg/K, ΔT=10 K
  Q = 418000 J
Heat Transfer
 Conduction
 Convection
 Latent Heating
 Radiation
 Advection
 You touch a warm pot on the stove and get a burn
 What is this form of heat transfer????
Conduction
 Heat will be transferred between two objects of different
temperatures when they are TOUCHING!
 Good conductors are better at transferring heat when
touching other molecules (many metals)
 Conduction determined by how good a conductor the
material is and how large the temperature difference is
between the objects
Winds blow in warmer air
What type of heat transfer is this?
Advection
Warm air advection when we expect the winds to warm our
region over time
 Air temperatures aloft increase because of the
movement of parcels near that ground that have been
warmed by the Earth
 What type of heat transfer is this?
Convection
Warm air is less dense than cooler air – so it rises
It rises until it has cooled (by expansion) to the surrounding
air’s temp
Important mechanism!!!!
Earth is heated by sun and atmosphere is warmed from
below by the Earth
 Causes convection
Ideal Gas Law Used:
 Parcel of air warmer than air around it –> will rise
 As it rises, pressure exerted on it by the surrounding air
decreases  Volume of parcel increases (expands)
 Temperature must then decrease
 Parcel cools as it is lifted!
 If cools to its dewpoint, will form cloud
 The sun warms the Earth, but they aren’t touching
 What mechanism is responsible for this???
Radiation
 All objects with temperature > 0 K emit radiation
 Temperature determines what wavelengths an object
emits – warmer objects emit more shorter wavelengths
than a cooler object
(λmax = 2897um/ T ) (Wien’s Law)
 Temp determines the amount of energy emitted by
radiation (E ~ T4) (Stephan-Boltzmann’s Law)
Radiation
Shorter wavelengths carry more energy!
 I am freezing cold after I get out of the swimming pool
 Why am I losing heat?
Latent Heat
 It takes energy to change water from a liquid to a gas
 Your body supplies that heat when you get out of the
pool and you cool off
 Why do you dry off faster in a desert climate?